Thermochemical state functions

Table 17.1. Relative Thermochemical State Functions of Usual Solvents ...

The enthalpy of formation of a compound is a so-called thermodynamic state function, which means that the value depends only on the initial and final states of the system. When the formation of crystalline NaCl from the elements is considered, it is possible to consider the process as if it occurred in a series of steps that can be summarized in a thermochemical cycle known as a Born-Haber cycle. In this cycle, the overall heat change is the same regardless of the pathway that is followed between the initial and final states. Although the rate of a reaction depends on the pathway, the enthalpy change is a function of initial and final states only, not the pathway between them. The Born-Haber cycle for the formation of sodium chloride is shown as follows ... 

State functions (Frame 1, section 1.5) are amenable to the construction of thermochemical cycles since provided that we can devise alternative routes between the same initial and final states, then the changes in state functions via these two alternative routes will be identical. 

The enthalpy is a state function for a change of state in a system, AH solely depends on the initial state and the final state of the system. This important property is e.g. used in thermochemical calculations that describe changes of enthalpy during chemical reactions or phase transitions. 

Figure 3.25. In thermochemical calculation it is utilized that the enthalpy H is a state function therefore, for a process connecting states of equilibrium, AH is independent of the process path (Hess s law).

The thermochemical calculation method is directly based on the fact that the enthalpy is a state function. The calculation principle is often referred to as Hess s law, since this principle was originally formulated as an empirical rule by the Swiss physicist G.H. Hess (1840). 

Cesium was first produced ia the metallic state by electrolysis of a molten mixture of cesium and barium cyanides (2). Subsequentiy the more common thermochemical—reduction techniques were developed (3,4). There were essentially no iadustrial uses for cesium until 1926, when it was used for a few years as a getter and as an effective agent ia reduciag the electron work function on coated tungsten filaments ia radio tubes. Development of photoelectric cells a few years later resulted ia a small but steady consumption of cesium and other appHcations for cesium ia photosensing elements followed. 

To make contact with atomic theories of the binding of interstitial hydrogen in silicon, and to extrapolate the solubility to lower temperatures, some thermodynamic analysis of these data is needed a convenient procedure is that of Johnson, etal. (1986). As we have seen in Section II. l,Eqs. (2) et seq., the equilibrium concentration of any interstitial species is determined by the concentration of possible sites for this species, the vibrational partition function for each occupied site, and the difference between the chemical potential p, of the hydrogen and the ground state energy E0 on this type of site. In equilibrium with external H2 gas, /x is accurately known from thermochemical tables for the latter. A convenient source is the... 

The principal feature of this relationship is that F values are derived solely from molecular formulae and chemical structures and require no prior knowledge of any physical, chemical or thermochemical properties other than the physical state of the explosive that is, explosive is a solid or a liquid [72]. Another parameter related to the molecular formulae of explosives is OB which has been used in some predictive schemes related to detonation velocity similar to the prediction of bri-sance, power and sensitivity of explosives [35, 73, 74]. Since OB is connected with both, energy available and potential end products, it is expected that detonation velocity is a function of OB. As a result of an exhaustive study, Martin etal. established a general relation that VOD increases as OB approaches to zero. The values of VOD calculated with the use of these equations for some explosives are given in the literature [75] and deviations between the calculated and experimental values are in the range of 0.46-4.0%. 

It is also important to keep in mind the independent (state) variables that were specified in deriving q. That is, the partition function was derived with the number of molecules N, the volume of the system V, and the temperature T specified as the independent variables. Thus, when taking the derivative with respect to temperature, as will be needed later, it is good to keep in mind that q = q(N, V, T). The partition function for the entire system of identical molecules, with independent variables N, V, and T, is denoted by a capital Q. If the molecules are indistinguishable, as would normally be the case when calculating thermochemical properties for a given species, then the system partition function is related to the molecular partition function by... 

A great number of studies related to thermochemical properties of QDO and PDO derivatives have been recently described by Ribeiro da Silva et al. [98-103]. These studies, which have involved experimental and theoretical determinations, have reported standard molar enthalpies of formation in the gaseous state, enthalpies of combustion of the crystalline solids, enthalpies of sublimation, and molar (N - O) bond dissociation enthalpies. Table 5 shows the most relevant determined parameters. These researchers have employed, with excellent results, calculations based in density functional theory in order to estimate gas-phase enthalpies of formation and first and second N - O dissociation enthalpies [103]. 

Based upon experimentally observed spectroscopic data, statistical thermodynamic calculations provide thermodynamic data which would not be obtained readily from direct experimental measurements for the species and temperature of interest to rocket propulsion. If the results of the calculations are summarized in terms of specific heat as a function of temperature, the other required properties for a particular specie, for example, enthalpy, entropy, the Gibb s function, and equilibrium constant may be obtained in relation to an arbitrary reference state, usually a pressure of one atmosphere and a temperature of 298.15°K. Or alternately these quantities may be calculated directly. Significant inaccuracies in the thermochemical data are not associated generaUy with the results of such calculations for a particular species, but arise in establishing a valid basis for comparison of different species. 

Xu X, Goddard III WA (2004b) The X3LYP extended functional for accurate description of nonbond interactions, spin states, and thermochemical properties, Proc Natl Acad Sci USA, 101 2673-2677... 

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